Related papers: Thomas--Wigner rotation as a holonomy for spin-$1/…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
We revisit the derivation of the nonlocal collision term in the Boltzmann equation for spin-1/2 particles, using both the Wigner-function approach by de Groot, van Leeuwen, and van Weert, and the Kadanoff-Baym equation in $T$-matrix…
In this work we analyze the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin-$\frac{1}{2}$ particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner…
The origin of the Thomas factor 1/2 in the spin-orbit hamiltonian can be understood by considering the case of a classical electron moving in crossed electric and magnetic fields chosen such that the electric Coulomb force is balanced by…
Because of its apparent complexity, the discussion of Wigner rotation is usually reduced to the study of Thomas precession, which is too specific a case to allow a deep understanding of boost composition. However, by simple arguments and…
Starting with the Chern-Simons formulation of (2+1)-dimensional gravity we show that the gravitational interactions deform the Poincare symmetry of flat space-time to a quantum group symmetry. The relevant quantum group is the quantum…
We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…
The Moyal formalism for a particle can be derived from the Moyal formalism for a spin. This is done by contracting the group of rotations to the oscillator group. A new derivation is given for the contraction of the spin Wigner-kernel to…
This note summarizes the physics and mathematics of Lorentz transformations for massless particles, specifically for photons. We provide a complete analytical derivation of Wigner's little group matrix and a closed formula for the…
Source-less wave equations are derived for massless scalar, neutrino and electromagnetic perturbations of a radiating Kerr space-time, and the Hawking radiation of massless particles with spin $s =0, 1/2$ and 1 in this geometry is…
We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…
We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in $\hbar$ it contains a nonlocal contribution, which is responsible for the…
Recently (Phys. Rev. Lett. 114 (2015), 210402) the influence of the so called "Wigner translations" (more generally-Lorentz trans- formations) on circularly polarized Gaussian packets ( providing the solution to Maxwell equations in…
Thin-shell wormholes are constructed starting from the exotic branch of Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations…
The higher-spin geometries of $W_\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic…
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the…
In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a "spin-shell" constraint from which the spin content can be read off. We extend this formalism to massive (super)particles…
We present a quantum kinetic theory for spin-$1/2$ particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in $\hbar$, based on a gauge-invariant Wigner transformation. Compared to previous…
The effect of the relativistic spin rotation on two--particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncolinear…
It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles…